In a standard quantum key distribution (QKD) scheme such as BB84, two procedures, error correction and privacy amplification, are applied to extract a final secure key from a raw key generated from quantum transmission. To simplify the study of protocols, it is commonly assumed that the two procedures can be decoupled from each other. While such a decoupling assumption may be valid for individual attacks, it is actually unproven in the context of ultimate or unconditional security, which is the Holy Grail of quantum cryptography. In particular, this means that the application of standard efficient two-way error-correction protocols like Cascade is not proven to be unconditionally secure. Here, I provide the first proof of such a decoupling principle in the context of unconditional security. The method requires Alice and Bob to share some initial secret string and use it to encrypt their communications in the error correction stage using one-time-pad encryption. Consequently, I prove the unconditional security of the interactive Cascade protocol proposed by Brassard and Salvail for error correction and modified by one-time-pad encryption of the error syndrome, followed by the random matrix protocol for privacy amplification. This is an efficient protocol in terms of both computational power and key generation rate. My proof uses the entanglement purification approach to security proofs of QKD. The proof applies to all adaptive symmetric methods for error correction, which cover all existing methods proposed for BB84. In terms of the net key generation rate, the new method is as efficient as the standard Shor-Preskill proof.
In a standard quantum key distribution (QKD) scheme such as BB84, two procedures, error correction and privacy amplification, are applied to extract a final secure key from a raw key generated from quantum transmission. To simplify the study of protocols, it is commonly assumed that the two procedures can be decoupled from each other. While such a decoupling assumption may be valid for individual attacks, it is actually unproven in the context of ultimate or unconditional security, which is the Holy Grail of quantum cryptography. In particular, this means that the application of standard efficient two-way error-correction protocols like Cascade is not proven to be unconditionally secure. Here, I provide the first proof of such a decoupling principle in the context of unconditional security. The method requires Alice and Bob to share some initial secret string and use it to encrypt their communications in the error correction stage using one-time-pad encryption. Consequently, I prove the unconditional security of the interactive Cascade protocol proposed by Brassard and Salvail for error correction and modified by one-time-pad encryption of the error syndrome, followed by the random matrix protocol for privacy amplification. This is an efficient protocol in terms of both computational power and key generation rate. My proof uses the entanglement purification approach to security proofs of QKD. The proof applies to all adaptive symmetric methods for error correction, which cover all existing methods proposed for BB84. In terms of the net key generation rate, the new method is as efficient as the standard Shor-Preskill proof.
We prove the unconditional security of the standard six-state scheme for quantum key distribution (QKD). We demonstrate its unconditional security up to a bit error rate of 12.7 percents, by allowing only one-way classical communications in the error correction/privacy amplification procedure between Alice and Bob. This shows a clear advantage of the six-state scheme over another standard scheme---BB84, which has been proven to be secure up to only about 11 percents, if only one-way classical communications are allowed. Our proof technique is a generalization of that of Shor-Preskill's proof of security of BB84. We show that a advantage of the six-state scheme lies in the Alice and Bob's ability to establish rigorously from their test sample the non-trivial mutual information between the bit-flip and phase error patterns. A modified version of the degenerate quantum codes studied by DiVincenzo, Shor and Smolin is employed in our proof.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secret-key agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Quantum key distribution (QKD) relies on quantum and classical procedures in order to achieve the growing of a secret random string -the key- known only to the two parties executing the protocol. Limited intrinsic efficiency of the protocol, imperfect devices and eavesdropping produce errors and information leakage from which the set of measured signals -the raw key- must be stripped in order to distill a final, information theoretically secure, key. The key distillation process is a classical one in which basis reconciliation, error correction and privacy amplification protocols are applied to the raw key. This cleaning process is known as information reconciliation and must be done in a fast and efficient way to avoid cramping the performance of the QKD system. Brassard and Salvail proposed a very simple and elegant protocol to reconcile keys in the secretkey agreement context, known as Cascade, that has become the de-facto standard for all QKD practical implementations. However, it is highly interactive, requiring many communications between the legitimate parties and its efficiency is not optimal, imposing an early limit to the maximum tolerable error rate. In this paper we describe a low-density parity-check reconciliation protocol that improves significantly on these problems. The protocol exhibits better efficiency and limits the number of uses of the communications channel. It is also able to adapt to different error rates while remaining efficient, thus reaching longer distances or higher secure key rate for a given QKD system.
Shor and Preskill (see Phys. Rev. Lett., vol.85, p.441, 2000) have provided a simple proof of security of the standard quantum key distribution scheme by Bennett and Brassard (1984) by demonstrating a connection between key distribution and entanglement purification protocols (EPPs) with one-way communications. Here, we provide proofs of security of standard quantum key distribution schemes, Bennett and Brassard and the six-state scheme, against the most general attack, by using the techniques of two-way entanglement purification. We demonstrate clearly the advantage of classical post-processing with two-way classical communications over classical post-processing with only one-way classical communications in quantum key distribution (QKD). This is done by the explicit construction of a new protocol for (the error correction/detection and privacy amplification of) Bennett and Brassard that can tolerate a bit error rate of up to 18.9%, which is higher than what any Bennett and Brassard scheme with only one-way classical communications can possibly tolerate. Moreover, we demonstrate the advantage of the six-state scheme over Bennett and Brassard by showing that the six-state scheme can strictly tolerate a higher bit error rate than Bennett and Brassard. In particular, our six-state protocol can tolerate a bit error rate of 26.4%, which is higher than the upper bound of 25% bit error rate for any secure Bennett and Brassard protocol. Consequently, our protocols may allow higher key generation rate and remain secure over longer distances than previous protocols. Our investigation suggests that two-way entanglement purification is a useful tool in the study of advantage distillation, error correction, and privacy amplification protocols.
Quantum key distribution (QKD) is a method that enables secure communication between two parties by applying the ideas of quantum physics. By minimizing information leakage that can happen during the key generation process, privacy amplification is a technique used to improve the security of QKD. The technique involves processing the raw key obtained from QKD through a randomization procedure to remove any residual information that may have been leaked during the quantum transmission. While privacy amplification can significantly improve the security of QKD, the effectiveness of the technique is limited by the quality of the initial raw key. The BB84 QKD protocol has been improved with the proposed En-BB84 protocol, which includes built-in authentication and integrity checks. The En-BB84 protocol ensures secure distribution of secret keys and protects against tampering by attackers. Key distillation and error correction techniques are employed to extract a shorter, more secure shared secret key and correct errors introduced during qubit transmission. The protocol utilizes a four-state QKD approach, expanding on the traditional two-state scheme of BB84. A simulation of the En-BB84 protocol is demonstrated using a quantum circuit implemented with Qiskit in Python. The circuit employs various gates and operations, including Hadamard, CX, controlled swap, and RZ gates, to achieve encoding and error correction. Furthermore, we have designed a better protocol with improved error rates by incorporating improvisations on the BB84 protocol. Experimental results indicate the successful integration of the B92 error correction scheme into the modified BB84 protocol, enhancing the security and performance of QKD systems.